[{"_1":2,"_207":-5,"_208":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/e0f0b998-a084-42f3-adf4-9668090511ab","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_50":51,"_52":53,"_73":195,"_196":197},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_45":17,"_46":47,"_48":49},"correctOptionId","","difficulty","id","e0f0b998-a084-42f3-adf4-9668090511ab","options",[23,29,33,37,41],{"_19":24,"_25":26,"_27":28},"b09e87f0-65b5-43e4-b21b-339706cd8e7a","label","A","text","15 N.",{"_19":30,"_25":31,"_27":32},"550e2705-bc4a-4f64-8955-bc21b2e02837","B","45 N.",{"_19":34,"_25":35,"_27":36},"d525bf34-5a09-4681-9631-66410bb85691","C","2123 N.",{"_19":38,"_25":39,"_27":40},"4b6ec203-ddf7-45e8-a902-8a7e891e5e17","D","102 N.",{"_19":42,"_25":43,"_27":44},"b9bf7e80-7387-407e-b277-7f4547dd178c","E","178,9 N.","solution_explanation","statement","Em um suporte tipo gancho, pendurado no teto de uma casa, atuam as forças F_1 = 75 \\, \text{N} e F_2 = 125 \\, \text{N}. Fazendo, respectivamente, ângulos de 20^{\text{°}} e 35^{\text{°}} com a vertical. A força resultante sobre ele é de aproximadamente:","status","pending_classification","relatedVideos",[],"similarQuestions",[54,121,138,155,175],{"_16":17,"_18":17,"_19":55,"_21":56,"_45":17,"_46":72,"_73":74},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[57,60,63,66,69],{"_19":58,"_25":26,"_27":59},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":61,"_25":31,"_27":62},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_19":64,"_25":35,"_27":65},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_19":67,"_25":39,"_27":68},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_19":70,"_25":43,"_27":71},"112831da-be9c-458e-94cb-e8292d0dba12","y'' - 2y' + 6y = 0","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

","tags",[75,98,107,114],{"_19":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":97},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","name","Engenharia Civil","alias","engenharia-civil","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","eb9315c5-bd04-4116-aa46-02c4fde320c0","created_at","2025-04-29T02:19:12.828432+00:00","updated_at","metadata",{"_90":91,"_92":93,"_94":95},"childrenCount",21,"content_count",0,"question_count",45865,"slug","engenharia-civil-3",{"_19":99,"_77":100,"_79":101,"_81":82,"_83":76,"_85":102,"_87":102,"_88":103,"_96":106},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_90":104,"_92":93,"_94":105},5,8852,"estruturas-1",{"_19":108,"_77":109,"_79":110,"_81":82,"_83":99,"_85":111,"_87":111,"_88":112,"_96":110},"e9d666f5-dcb8-4aa3-abc7-27cfb929e3b6","Análise Estrutural","analise-estrutural","2025-04-29T04:00:06.9766+00:00",{"_90":93,"_92":93,"_94":113},4694,{"_19":84,"_77":115,"_79":116,"_81":82,"_83":-5,"_85":117,"_87":117,"_88":118,"_96":116},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_90":119,"_92":93,"_94":120},29,351586,{"_16":17,"_18":17,"_19":122,"_21":123,"_45":17,"_46":136,"_73":137},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[124,127,130,133],{"_19":125,"_25":26,"_27":126},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":128,"_25":31,"_27":129},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":131,"_25":35,"_27":132},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":134,"_25":39,"_27":135},"1f5e395b-c362-4503-8261-dcfcae96b1ce","Falso, verdadero, verdadeiro, verdadeiro.","

Divide el polinomio p(x) = 3x^4 + 4x^3 + x^2 entre el polinomio q(x) = 2+x. Como el polinomio divisor, q(x), es de grado 2, debemos encontrar dos polinomios, un polinomio cociente (c(x)) y un polinomio resto (r(x)) de grado 1 o 0, tales que p(x) = q(x) * c(x) + r(x).

El polinomio p(x) es de grado 4.

El polinomio q(x) es de grado 1.

El polinomio cociente c(x) es de grado 2.

El polinomio resto r(x) es de grado 1 o 0.

",[75,98,107,114],{"_16":17,"_18":17,"_19":139,"_21":140,"_45":17,"_46":153,"_73":154},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[141,144,147,150],{"_19":142,"_25":26,"_27":143},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":145,"_25":31,"_27":146},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":148,"_25":35,"_27":149},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":151,"_25":39,"_27":152},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[75,98,107,114],{"_16":17,"_18":17,"_19":156,"_21":157,"_45":17,"_46":173,"_73":174},"996628fc-4ac3-4821-86bd-839f86a97a6d",[158,161,164,167,170],{"_19":159,"_25":26,"_27":160},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":162,"_25":31,"_27":163},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":165,"_25":35,"_27":166},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":168,"_25":39,"_27":169},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":171,"_25":43,"_27":172},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[75,98,107,114],{"_16":17,"_18":17,"_19":176,"_21":177,"_45":17,"_46":193,"_73":194},"c478a46c-46a8-4942-ae14-2e79def3dda2",[178,181,184,187,190],{"_19":179,"_25":26,"_27":180},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":182,"_25":31,"_27":183},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":185,"_25":35,"_27":186},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":188,"_25":39,"_27":189},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":191,"_25":43,"_27":192},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[75,98,107,114],[75,98,107,114],"tagsTree",[198],{"_19":84,"_77":115,"_79":116,"_81":82,"_83":-5,"_85":117,"_87":117,"_88":118,"_96":116,"_199":200},"children",[201],{"_19":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":97,"_199":202},[203],{"_19":99,"_77":100,"_79":101,"_81":82,"_83":76,"_85":102,"_87":102,"_88":103,"_96":106,"_199":204},[205],{"_19":108,"_77":109,"_79":110,"_81":82,"_83":99,"_85":111,"_87":111,"_88":112,"_96":110,"_199":206},[],"actionData","errors"]

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